Power diagrams: properties, algorithms and applications
SIAM Journal on Computing
On the computational geometry of pocket machining
On the computational geometry of pocket machining
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Computer Aided Geometric Design
Voronoi diagram of a circle set from Voronoi diagram of a point set: topology
Computer Aided Geometric Design
Voronoi diagram of a circle set from Voronoi diagram of a point set: geometry
Computer Aided Geometric Design
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Updating the topology of the dynamic Voronoi diagram for spheres in Euclidean d-dimensional space
Computer Aided Geometric Design
Proximity and applications in general metrics
Proximity and applications in general metrics
SFCS '75 Proceedings of the 16th Annual Symposium on Foundations of Computer Science
Efficient computation of continuous skeletons
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
Medial Axis Transformation of a Planar Shape
IEEE Transactions on Pattern Analysis and Machine Intelligence
An efficient algorithm for three-dimensional β-complex and β-shape via a quasi-triangulation
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Molecular surfaces on proteins via beta shapes
Computer-Aided Design
Computing the Voronoi cells of planes, spheres and cylinders in R3
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Triangulation of molecular surfaces
Computer-Aided Design
Computing the Voronoi cells of planes, spheres and cylinders in R3
Computer Aided Geometric Design
Region-expansion for the Voronoi diagram of 3D spheres
Computer-Aided Design
Computer-Aided Design
Interaction interfaces in proteins via the Voronoi diagram of atoms
Computer-Aided Design
A sweepline algorithm for Euclidean Voronoi diagram of circles
Computer-Aided Design
Manifoldization of β-shapes in O(n) time
Computer-Aided Design
Real-time triangulation of molecular surfaces
ICCSA'07 Proceedings of the 2007 international conference on Computational science and its applications - Volume Part I
Multi-resolution protein model
ICCSA'07 Proceedings of the 2007 international conference on Computational science and Its applications - Volume Part II
Topologies of surfaces on molecules and their computation in O(n) time
Computer-Aided Design
Quasi-worlds and quasi-operators on quasi-triangulations
Computer-Aided Design
Three-dimensional beta-shapes and beta-complexes via quasi-triangulation
Computer-Aided Design
3D Voronoi diagrams of real trees
Journal of Computing Sciences in Colleges
Protein-ligand docking based on beta-shape
Transactions on computational science IX
Protein-ligand docking based on beta-shape
Transactions on computational science IX
Power diagrams and intersection detection
ICCSA'11 Proceedings of the 2011 international conference on Computational science and its applications - Volume Part III
Querying simplexes in quasi-triangulation
Computer-Aided Design
A β-shape from the Voronoi diagram of atoms for protein structure analysis
ICCSA'06 Proceedings of the 6th international conference on Computational Science and Its Applications - Volume Part I
Reduction of the search space in the edge-tracing algorithm for the voronoi diagram of 3d balls
ICCSA'06 Proceedings of the 6th international conference on Computational Science and Its Applications - Volume Part I
Euclidean voronoi diagrams of 3d spheres: their construction and related problems from biochemistry
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
QTF: Quasi-triangulation file format
Computer-Aided Design
Geometry guided crystal phase transition pathway search
Computer-Aided Design
Anomalies in quasi-triangulations and beta-complexes of spherical atoms in molecules
Computer-Aided Design
Visualization for the Physical Sciences
Computer Graphics Forum
Protein structure optimization by side-chain positioning via beta-complex
Journal of Global Optimization
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Despite its important applications in various disciplines in science and engineering, the Euclidean Voronoi diagram for spheres, also known as an additively weighted Voronoi diagram, in 3D space has not been studied as much as it deserves. In this paper, we present an algorithm to compute the Euclidean Voronoi diagram for 3D spheres with different radii. The presented algorithm follows Voronoi edges one by one until the construction is completed in O(mn) time in the worst-case, where m is the number of edges in the Voronoi diagram and n is the number of spherical balls. As building blocks, we show that Voronoi edges are conics that can be precisely represented as rational quadratic Bezier curves. We also discuss how to conveniently represent and process Voronoi faces which are hyperboloids of two sheets.